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It is well-known that linear quadratic regulators (LQR) enjoy guaranteed stability margins, whereas linear quadratic Gaussian regulators (LQG) do not. In this letter, we consider systems and compensators defined over directed acyclic graphs. In particular, there are multiple decision-makers, each with access to a different part of the global state. In this setting, the optimal LQR compensator is dynamic, similar to classical LQG. We show that when sub-controller input costs are decoupled (but there is possible coupling between sub-controller state costs), the decentralized LQR compensator enjoys similar guaranteed stability margins to classical LQR. However, these guarantees disappear when cost coupling is introduced.
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Meta-learning linear quadratic regulators: a policy gradient MAML approach for model-free LQR
We investigate the problem of learning linear quadratic regulators (LQR) in a multi-task, heterogeneous, and model-free setting. We characterize the stability and personalization guarantees of a policy gradient-based (PG) model-agnostic meta-learning (MAML) (Finn et al., 2017) approach for the LQR problem under different task-heterogeneity settings. We show that our MAML-LQR algorithm produces a stabilizing controller close to each task-specific optimal controller up to a task-heterogeneity bias in both model-based and model-free learning scenarios. Moreover, in the model-based setting, we show that such a controller is achieved with a linear convergence rate, which improves upon sub-linear rates from existing work. Our theoretical guarantees demonstrate that the learned controller can efficiently adapt to unseen LQR tasks.
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- Award ID(s):
- 2231350
- PAR ID:
- 10542303
- Editor(s):
- Abate, A; Cannon, M; Margellos, K; Papachristodoulou, A
- Publisher / Repository:
- Proceedings of Machine Learning Research (PMLR)
- Date Published:
- Volume:
- 242
- Page Range / eLocation ID:
- 902-915
- Format(s):
- Medium: X
- Location:
- Oxford, United Kingdom
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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